k>1
Image is larger and on the same rays.
🎯 Learning Objectives
- enlarge figures from the origin or another centre;
- use positive, fractional and negative scale factors;
- find scale factor and centre;
- describe enlargement completely.
Introduction
This lesson develops Enlargements from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Complete Description
Enlargement = centre of enlargement + scale factor.
0<k<1
Image is smaller and on the same rays.
k<0
Image lies on the opposite side of the centre.
Coordinates About the Origin
(x,y)→(kx,ky).
For k=2, (3,−1)→(6,−2).
Finding the Centre
Join corresponding vertices and extend the lines. Their common intersection is the centre of enlargement.
Practice Questions
- Enlarge (2,−3) by scale factor 3 about the origin.
- Enlarge (8,4) by scale factor 1/2 about the origin.
- What does scale factor −2 mean?
- An object side is 4 cm and image side is 10 cm. Find k.
✅ Check Your Work
Show answers and working
- (6,−9).
- (4,2).
- Twice the size, with corresponding points on the opposite side of the centre.
- k=10/4=2.5.
🧠 Learn It Visually: Enlargements
An enlargement changes every distance from a fixed centre by the same multiplier called the scale factor. It may make a figure larger, smaller or place it on the opposite side of the centre.
Centre of enlargement
Object point, centre and image point lie on one straight ray.
Scale factor k
Image distance from centre = |k| × object distance.
Negative or fractional k
A fraction shrinks. A negative factor places the image on the opposite side and reverses direction through the centre.
🎛️ See the Transformation Happen
Select an option and watch the object change. Compare orientation, size and position.
Choose a transformation.
Think Like a Mathematician: Can an enlargement with scale factor 1 move a shape?
🧷 Remember
Lengths multiply by |k|, areas multiply by k², and angles stay unchanged.
⚠️ Common Mistake
Measuring scale factor from the origin instead of from the stated centre.
🎯 Exam Tip
To find the centre, join at least two pairs of corresponding vertices and extend the lines until they meet.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.